Virtually unheard of prior to 1990, the use of living donors for liver transplantation has been increasing and now represents over 500 transplants per year. Although living donor transplantation has several potential advantages, the procedure places the living donor at risk of death and morbidity and, therefore, should be undertaken as appropriately and efficiently as possible. In this exploratory application, we propose to use Markov decision processes, (MDPs, which are mathematical tools specifically designed to analyze sequential decisions under conditions of uncertainty) to evaluate the optimal timing of living donor liver transplantation. The overall goal of this developmental R21 application is to provide insights into the factors that affect this timing decision so that transplant decisions can be made as carefully and successfully as possible. Specifically, this work seeks to fulfill two specific aims: Aim 1: Evaluate the optimal time to transplant a living donor liver given the characteristics of the recipient and donor. Acceptance of a living donor organ occurs outside of the UNOS waiting list and is not subject to external allocation and selection rules. Therefore, the only decision to be made is the appropriate time (in clinical terms of declining health status) to conduct the transplant. We propose to build an MDP that will evaluate this question. Aim 2: Evaluate the optimal waiting time for a cadaveric transplant prior to accepting a living donor transplant. Because the existence of a willing potential living donor does not preclude listing on the cadaveric wait list, and because a prospective recipient may not want to place that donor at mortal risk, the more realistic question is: "How long should I wait on the cadaveric list before accepting a living donor?" The MDP developed in AIM 1 will be enhanced to incorporate the sequential possibility of being offered cadaveric organs of varying quality. The work is innovative and developmental as MDPs have not typically been used to evaluate medical decisions, even though they were specifically developed to evaluate sequential decisions under uncertainty (which aptly describes most decisions clinicians make). The investigative team has substantial and unique experience in modeling the progression of liver disease and the transplant process, and the application of mathematical models from management science to problems in health and medicine. We seek to extend our history of successful collaboration between Medicine and Industrial Engineering, to investigate the usefulness of these sophisticated mathematical models when applied to a real and complex medical decision.